ISA 444/544: Business Forecasting

.title[
# ISA 444/544: Business Forecasting
]
.subtitle[
## 01: Introduction to Time Series Analysis and Forecasting
]
.author[
### <br>Fadel M. Megahed, PhD <br><br> Raymond E. Glos Professor in Business <br> Farmer School of Business<br> Miami University<br><br> <a href="https://twitter.com/FadelMegahed"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z" /></svg> <span class="citation">@FadelMegahed</span></a> <br> <a href="https://github.com/fmegahed/"><svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" /></svg> fmegahed</a> <br> <a href="mailto:fmegahed@miamioh.edu"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z" /></svg> fmegahed@miamioh.edu</a><br> <a href="https://calendly.com/fmegahed"><svg viewBox="0 0 384 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M202.021 0C122.202 0 70.503 32.703 29.914 91.026c-7.363 10.58-5.093 25.086 5.178 32.874l43.138 32.709c10.373 7.865 25.132 6.026 33.253-4.148 25.049-31.381 43.63-49.449 82.757-49.449 30.764 0 68.816 19.799 68.816 49.631 0 22.552-18.617 34.134-48.993 51.164-35.423 19.86-82.299 44.576-82.299 106.405V320c0 13.255 10.745 24 24 24h72.471c13.255 0 24-10.745 24-24v-5.773c0-42.86 125.268-44.645 125.268-160.627C377.504 66.256 286.902 0 202.021 0zM192 373.459c-38.196 0-69.271 31.075-69.271 69.271 0 38.195 31.075 69.27 69.271 69.27s69.271-31.075 69.271-69.271-31.075-69.27-69.271-69.27z" /></svg> Automated Scheduler for Office Hours</a><br><br>
]
.date[
### Fall 2025
]

---

# Learning Objectives for Today's Class

- Describe the role of forecasting in business.

- Describe the key components of a **time-series** (**trend**, **seasonality**, **multiple seasonality**, and **cycles**).

- Explain the concept of data-generating process (DGP)

- Discuss limits of forecasting

- Understand key forecasting terminology

---
class: inverse, center, middle

# Course Motivation

---

## Forecasting Impacts Everything and Everyone

.pull-left[
- **Businesses**: Sales forecasts set revenue targets, inventory projections optimize supply chains, and staffing plans ensure workforce readiness during demand fluctuations.

- **Gov.**: Tax revenue and social programs forecasts aid budgeting and resource allocation.

- **Individuals**: Financial forecasts support budgeting, saving, and retirement planning.

- **Weather**: Forecast inform agriculture, disaster prep, and daily decisions.

]

.font80[Source: [Congressional Budget Office](https://www.cbo.gov/publication/61172#_idTextAnchor040)]

<a class="weatherwidget-io" href="https://forecast7.com/en/39d47n84d75/45056/" data-label_1="OXFORD" data-label_2="WEATHER" data-theme="original" >OXFORD WEATHER</a>
<script>
!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0];if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src='https://weatherwidget.io/js/widget.min.js';fjs.parentNode.insertBefore(js,fjs);}}(document,'script','weatherwidget-io-js');
</script>
.font80[Source: [Weather Widget's Forecast](https://weatherwidget.io/)]
</center>

]

---

## Microsoft's Missed Opportunity with Mobile Phones

.font90[
> **Q**: People get passionate when Apple comes out with something new—the iPhone; of course ... **Is that something you'd want them to feel about Microsoft?**

<br>

> **A**: It's sort of a funny question. **Would I trade 96% of the market for 4%?** *(Laughter.)*

> **I want to have products that appeal to everybody.** There's no chance that the iPhone is going to get any significant market share. **No chance.** It's a $500 subsidized item. They may make a lot of money.

> But if you actually take a look at the 1.3 billion phones that get sold, **I'd prefer to have our software in 60% or 70% or 80% of them**, than I would **2% or 3%, which is what Apple might get**.

]
]

.pull-right-2[
.center[
![Steve Ballmer](data:image/png;base64,#../../figures/ceo-ballmerx-large.jpg)

.font90[
Steve Ballmer, Former CEO of Microsoft in his infamous interview with [USA Today 2007](https://web.archive.org/web/20070502033654/https://www.usatoday.com/money/companies/management/2007-04-29-ballmer-ceo-forum-usat_N.htm)
]
]
]

---

## Microsoft's Missed Opportunity: Back of a Napkin Calc.

- Since Q1 2009, **Windows' Mobile OS's market share <= 2.5%**, and is now at 0.02% ([StatCounter](https://gs.statcounter.com/os-market-share/mobile/worldwide/#quarterly-200901-202403)).

- **Apple's Mobile iOS market share > 19%**, and is now at **27.69%** ([StatCounter](https://gs.statcounter.com/os-market-share/mobile/worldwide/#quarterly-200901-202403)).

- Apple's **iPhone revenues** from 2007 to 2024 was **$2.037 trillion** (per [statista](https://www.statista.com/statistics/263402/apples-iphone-revenue-since-3rd-quarter-2007/)).

- Assuming Microsoft could have captured just **5%** of Apple's market revenue `$\rightarrow$` **$102 billion**.

- This estimate **excludes app store and brand value**, which will make the missed opportunity even larger.
]

]

</div>

]

---

## Other Real-World Forecasting Failures in Tech

.pull-left[
  .center[
  
  <img src="data:image/png;base64,#../../figures/1024px-Ibm_px_xt_color.jpg" alt="IBM PC" style="width: auto; height: 190px" />
  
 .font80[**IBM**: Missed the PC revolution.]

]
]

.pull-right[
  .center[
  
  <img src="data:image/png;base64,#../../figures/The_Last_Blockbuster_storefront.jpg" alt="Blockbuster" style="width: auto; height: 190px;" />
  
  .font80[**Blockbuster**: Missed the streaming revolution.]

<img src="data:image/png;base64,#../../figures/Ysearch_2005.png" alt="Yahoo Logo" style="width: auto; height: 190px;" />
 
  .font80[**Yahoo**: Missed the search engine revolution.]
 
]

]

---

## Non-Tech Failures: Red Lobster's Endless Shrimp

.center[
  <img src="data:image/png;base64,#../../figures/red_lobster.png" alt="Red Loster endless shrimp deal was too popular; a key reason for the company's 11 million dollar loss in the third quarter of 2023" style="width: auto; height: 525px;" />
]

---

## Non-Tech Failures: Target's Overestimation

.center[
  <img src="data:image/png;base64,#../../figures/target.png" alt="Target Stock Plunges 21% on Weak Sales Ahead of Holiday Season" style="width: auto; height: 525px;" />
]

---

## Why Do These Stories Matter?

**(1) Forecasting Errors = Real Money Lost**  
  - **Microsoft**: $102 billion in potential mobile phone revenues.
  - **Target:** .bold[Overestimation] leads to unsold stock or overservicing (e.g., [Target's Stock Plunging by 21% due to lower profit and larger inventories](https://www.nytimes.com/2024/11/20/business/target-earnings-holiday-shopping.html?unlocked_article_code=1.sU4.BN7Y.DRvnq7F_52NO&smid=url-share)).
  - **Red Lobster**: $11M in losses due to .bold[underestimating] demand for their endless shrimp deal.

<br>

**(2) Course Relevance:**

This class will teach you how to identify .black[.bold[trends]], .black[.bold[seasonality]], and .black[.bold[cycles]], and .black[.bold[how to apply forecasting tools and models]] so you can **avoid these pitfalls** in your future roles. The goal is to allow you to make **data-driven forecasts**, not just gut-based decisions, and more importantly, be able to **quantify the uncertainty** in your forecasts.

---

## Can you Avoid Common Forecasting Mistakes?

- **Scenario**: You are a business analyst at a hotel chain.

- **Problem**: You are tasked with forecasting hotel occupancy for the next 11 months.

- **Data**: You have access to the hotel's monthly room occupancy data from 2022 to January of 2025. Download the file [here]https://miamioh.instructure.com/courses/240425/files/36340085?module_item_id=6161473).

- **Task:** .black[.bold[Without the use of any AI tools]], create a forecast for the hotel's occupancy for the next 11 months. The forecast can be made in Excel, R, or Python. .black[.bold[Document the process and the rationale behind your forecasts.]]

- **Non-graded Class Activity:** Input your logic for the 11-month forecast, and your quantitative forecast for **February 2025** in the next 2 tabs, respectively.

]

Use the editable text-box below to describe your logic for forecasting the hotel's occupancy for the next 11 months. Use bullet points to list your steps.

.can-edit.key-activity1_logic[

**Steps Taken to Generate the Forecasts:** .font70[(Insert below)]

- Edit me  
  
  - ... 
  
  - ...
]

]

- Input your solution for **February 2025** by using the QR code below.

]

]

<details>
  <summary>Let us discuss how to approach such a problem. </summary>

.can-edit.key-activity1_viz[

**Fadel's approach to this problem:** .font70[(To be discussed in class)]

- Edit me  
  
  - ... 
  
  - ...
]

]

<details>
  <summary>Let us think of a reasonable solution, which assumes no prior time-series knowledge. </summary>

<small>

```{python 
import pandas as pd

df_hotel = (
  pd.read_csv("../../data/01_hotel_occupancy.csv")
  .assign(date = lambda x: pd.to_datetime(x['date']),
    year = lambda x: x['date'].dt.year  )  )

# plotting of the data hidden for brevity

# compute the average occupancy per year and year-over-year growth rate
yearly_avg = df_hotel.groupby('year')['hotel_occupancy'].mean().drop(2025)
yoy_growth = yearly_avg.pct_change().mean()

monthly_2024 = df_hotel.query("year == 2024") # filter the data for 2024

# forecast the occupancy for 2025
forecast = pd.DataFrame({
    "date": pd.date_range(start="2025-01-01", end="2025-12-01", freq="MS"),
    "forecasted_occupancy": (monthly_2024['hotel_occupancy'] * (1 + yoy_growth) ).round(0).astype(int)
})

forecast.iloc[0:2].reset_index(drop=True)

</small> </details>
```

]
]

---

# Types of Data Over Time and the Components of a Time Series

---

## Cross-Sectional Data

**Cross-sectional data** captures multiple variables at a single point in time for each
observation; e.g., .bold[all the variables within a given observation] in the [DoL's LCA Disclosure Data for 2025 Q3](https://www.dol.gov/sites/dolgov/files/ETA/oflc/pdfs/LCA_Disclosure_Data_FY2025_Q3.xlsx) were collected simultaneously.

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Inc.","TANA SYSTEMS INC","Technumen, Inc.","L&T Technology Services Limited","Tata Consultancy Services Limited","Tata Consultancy Services Limited","QUANTUM TECHNOLOGIES LLC","GMA SOFT INC.","Tata Consultancy Services Limited","Oracle America, Inc.","Accenture LLP","SMACT Works, Inc.","Technumen, Inc.","BDG Wrap-Tite, Inc.","L&T Technology Services Limited","Ohio Valley Physicians, Inc.","The Kroger Company","Wailea Systems LLC","TATA CONSULTANCY SERVICES LIMITED","L&T Technology Services Limited","Hadiamondstar Software Solutions LLC","Clopay Corporation","LTIMindtree Limited","Tata Consultancy Services Limited","COGNIZANT TECHNOLOGY SOLUTIONS US CORP","Miami University","Alten Technology USA, Inc.","META SOFT INC","COGNIT AI INC","Precision eControl, LLC","The Kroger Company","The Christ Hospital Physicians LLC","Technology Hub Inc","Cardinal Health","QUANTUM TECHNOLOGIES LLC","CRYSTAL PROJECT, INC.","Tribco Inc.","OhioHealth Physician Group, Inc.","Arche Resources LLC","Shark Analytics LLC","QlikTech Inc.","KSOFT SYSTEMS INC","Cleveland Clinic Foundation","Tagma Solutions, Inc.","ANGSTROM FIBER SIDNEY","Bright Machines, Inc.","Cleveland Clinic Foundation","Cleveland Clinic Foundation","Cintas Corporation","Cleveland Clinic Foundation","Cleveland Clinic Foundation","Ams Tec Solutions LLC","DATAMART SYSTEMS, INC.","Tata Consultancy Services Limited","Winsupply Inc","Jones & Henry Engineers, Ltd.","Exact Benefits Group LLC.","OhioHealth Corp.","OCLC, Inc.","KSOFT SYSTEMS INC","Technology Hub Inc","Aries Computer Systems, Inc.","LTIMindtree Limited","LTIMindtree Limited","TRI-TECH LABORATORIES, LLC","Tata Consultancy Services Limited","Premier Renal Care Associates, LLC","SIPTEK GROUP INC","Tribco Inc.","TECHQUEST SOLUTIONS, LLC.","Horizon IT Inc","American Analyst, Inc.","TECHQUEST SOLUTIONS, LLC.","Mytee LLC","B D G WRAP-TITE, INC.","Lambdanets Inc","TATA CONSULTANCY SERVICES LIMITED","Cleveland Clinic","Tata Consultancy Services Limited","V-Soft Consulting Group, INC","MSAII LLC","The Ohio State University","Great Lakes Cheese Co. Inc.","Tata Consultancy Services Limited","DATAMETRICS SOFTWARE SYSTEMS, INC","JPMorgan Chase & Co.","Mettler-Toledo, LLC","Capgemini America Inc","Tata Consultancy Services Limited","MSAII LLC","SYSTEM SOFT TECHNOLOGIES, LLC","Progressive Casualty Insurance Company","CommuteAir LLC","The Ohio State University","The Ohio State University","Quadrant Technologies LLC","The Ohio State University","MSAII LLC","Vertiv Corporation","Wellness Card LLC","La Salle High School","Exel, Inc.","Tata Consultancy Services Limited","Luxottica of America Inc.","Cleveland Clinic","Highland Health Providers Corp.","MSAII LLC","MSAII LLC","Caprus IT Inc","The Ohio State University","Intelligrated Systems, Inc.","MSAII LLC","Dayton Osteopathic Hospital","Genpact LLC","Truist Bank","Tata Consultancy Services Limited","WORK FOR PRO INC.","Navvis & Company, LLC","Kenyon College","The Ohio State University","HM Health Solutions, Inc.","Tata Consultancy Services Limited","Cleveland Clinic Foundation","The Kroger Company","The Kroger Company","The Ohio State University","United Services Automobile Association","DATAMETRICS SOFTWARE SYSTEMS, INC","COMPUNNEL SOFTWARE GROUP, INC","ERP Analysts, Inc.","Congensys Corp.","The Ohio State University","VISTALTECH INC","U.S. Bank National Association","The Kroger Company","MSAII LLC","Emplifi Inc.","The Ohio State University","HORIZON EDUCATIONAL SERVICES OF COLUMBUS INC","MSAII LLC","Cleveland Clinic Foundation","Muskingum University","TATA CONSULTANCY SERVICES LIMITED","MSAII LLC","Tata Consultancy Services Limited","Mphasis Corporation","The Ohio State University"],["OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH"],[98004,63100,123000,211273,72000,82514,44000,211273,79950,490000,103000,103700,119954,95139,185585.95,102627,76000,86507,495000,86000,73000,86000,162493,59000,88179.23,150700,137400,136125,85000,75500,95742,75619,75000,99001.75999999999,151300,111010,102627,83243,137600,167000,95139,61008,51700,70387,137600,137600,55000,130000,62022,102630,73000,70000,83242,630000,78280,161000,86500,77438,203800,73000,120001,93000,136125,136125,62483,107619,136125,180305.6,223800,85000,115001,62500,93000,315000,126357.28,85900,102950,93242,93226,141398.66,161907,136125,100235,76000,107000,90000,89419,155000,136979.7,239200,65147,175000,62483,81250,52499,331000.02,102000,102700,230000,73000,77137,95000,74000.00999999999,120000,280500,620000,130541,82826,355000,77438,70000,102200,150000,75545,62506.19,76939.2,115803.57,73000,65147,103418,126204,132628,92000,137600,260000,102627,52499,72000,67683,78400,74000,85000,140000,90000,137600,490000,136125,103000,90000,61008,158700,137590,95139,172000,114288.92,126618,102200,90000,125000,90300,113855,105000,348741,90000,72862,90000,120000,60000,75200,156743.66,102200,173184,550000,230000,121000,90000,105997,134247,92846,90000,62960,84090,130490,102950,103000,132241.95,94391,56800,113568,137600,115500,142773.5,124906.81,58488,166950,95139,95000,103210,103000,386112,102627,115500,141384.93,90000,96600,67800,64820,90000,340000,55980,102200,85000,102200,126750,94000]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th>Date<\/th>\n      <th>Job Title<\/th>\n      <th>Employer<\/th>\n      <th>WORKSITE_STATE<\/th>\n      <th>Salary<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":7,"columnDefs":[{"targets":4,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatCurrency(data, \"$\", 0, 3, \",\", \".\", true, null);\n  }"},{"className":"dt-right","targets":4},{"name":"Date","targets":0},{"name":"Job Title","targets":1},{"name":"Employer","targets":2},{"name":"WORKSITE_STATE","targets":3},{"name":"Salary","targets":4}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[7,10,25,50,100]},"selection":{"mode":"multiple","selected":null,"target":"row","selectable":null}},"evals":["options.columnDefs.0.render"],"jsHooks":[]}</script>

]

---

## Time Series Data

**Time series data** captures a single variable at multiple points in time; e.g., the [daily stock prices for Apple](https://finance.yahoo.com/quote/AAPL/history?p=AAPL) or our **simulated monthly hotel room occupancy** dataset.

---

## Panel Data

**Panel data** captures multiple variables at multiple points in time for each observation; e.g., the [Panel Study of Income Dynamics](https://psidonline.isr.umich.edu/) or the [World Bank's World Development Indicators](https://databank.worldbank.org/source/world-development-indicators).

.font80[
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]

**Source:** Data queried from the [World Bank Data](https://datacatalog.worldbank.org/) using the [wbstats](https://cran.r-project.org/web/packages/wbstats/wbstats.pdf) <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:gold;overflow:visible;position:relative;"><path d="M50.7 58.5L0 160H208V32H93.7C75.5 32 58.9 42.3 50.7 58.5zM240 160H448L397.3 58.5C389.1 42.3 372.5 32 354.3 32H240V160zm208 32H0V416c0 35.3 28.7 64 64 64H384c35.3 0 64-28.7 64-64V192z"/></svg> in R. The printed results show a snapshot of 7 variables (out of a much larger panel dataset). You can think of panel data as a cross-sectional dataset with a longitudinal/time component.
]

---

## Components of Time Series Data: Trend

- **Trend**: A long-term increasing or decreasing pattern over time.

- **Example**: The [US GDP](https://fred.stlouisfed.org/series/GDP) has a long-term upward trend.

---

## Components of Time Series Data: Seasonality

**Seasonality** refers to the property of a time series that displays REGULAR patterns that repeat at a constant frequency (*m*). For example, the [number of retail trade workers](https://fred.stlouisfed.org/series/CEU4200000001) has a seasonal pattern (with an upward trend).

---

## Components of Time Series Data: Multiple Seasonality

**Multiple seasonality** refers to the property of a time series that displays multiple seasonal patterns that repeat at different frequencies.

---

## Components of Time Series Data: Cycles

**Cycles** refer to the property of a time series that displays irregular patterns that repeat at irregular frequencies. For example, the [US Total Vehicle Sales](https://fred.stlouisfed.org/series/TOTALSA) has business cycles that are influenced by economic conditions and advancements in vehicle technologies.

---

## Components of Time Series Data: Cycles

---

# Kahoot Competition #01

To assess your understanding and retention of the topics covered so far, you will **compete in a Kahoot competition (consisting of 5 questions)**:

- Go to <https://kahoot.it/>

- Enter the game pin, which will be shown during class

- Provide your first (preferred) and last name

- Answer each question within the allocated 20-second window (**fast and correct answers provide more points**)

<br>

**Winning the competition involves having as many correct answers as possible AND taking the shortest duration to answer these questions.** The winner <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:gold;overflow:visible;position:relative;"><path d="M400 0H176c-26.5 0-48.1 21.8-47.1 48.2c.2 5.3 .4 10.6 .7 15.8H24C10.7 64 0 74.7 0 88c0 92.6 33.5 157 78.5 200.7c44.3 43.1 98.3 64.8 138.1 75.8c23.4 6.5 39.4 26 39.4 45.6c0 20.9-17 37.9-37.9 37.9H192c-17.7 0-32 14.3-32 32s14.3 32 32 32H384c17.7 0 32-14.3 32-32s-14.3-32-32-32H357.9C337 448 320 431 320 410.1c0-19.6 15.9-39.2 39.4-45.6c39.9-11 93.9-32.7 138.2-75.8C542.5 245 576 180.6 576 88c0-13.3-10.7-24-24-24H446.4c.3-5.2 .5-10.4 .7-15.8C448.1 21.8 426.5 0 400 0zM48.9 112h84.4c9.1 90.1 29.2 150.3 51.9 190.6c-24.9-11-50.8-26.5-73.2-48.3c-32-31.1-58-76-63-142.3zM464.1 254.3c-22.4 21.8-48.3 37.3-73.2 48.3c22.7-40.3 42.8-100.5 51.9-190.6h84.4c-5.1 66.3-31.1 111.2-63 142.3z"/></svg> of the competition will receive a **0.15 bonus on Assignment 01**. Good luck!!!

**P.S:** The Kahoot competition will have **no impact on your grade**. It is a **fun** way of assessing your knowledge, motivating you to ask questions about topics covered that you do not have a full understanding of it, and providing me with some data that I can use to pace today's class. 
]

---

# The Data Generating Process

---

## The Idea of a Data Generating Process (DGP)

- A **time series** is defined as a **sequence of observations** recorded at regular time intervals.

- Any time series is generated by some kind of mechanism, which is often referred to as a **data generating process (GDP)**. For example, the hotel occupancy dataset is impacted by:   
  - .black[.bold[season]], .black[.bold[holidays]], .black[.bold[economic conditions]], and .black[.bold[marketing campaigns]];  
  - .black[.bold[number of rooms]], .black[.bold[room rates]], and .black[.bold[customer satisfaction]];   
  - .black[.bold[weather]], .black[.bold[local events]], and .black[.bold[competition]]; and 
  - .black[.bold[number of rooms already booked]], .black[.bold[room cancellations]], and .black[.bold[no-shows]].

- The **DGP** is the **underlying theoretical mechanism** that generates the data we observe.  
   - Accounts for both systematic patterns (e.g., trend, seasonality) and randomness.    
- **But**: In real-world settings, there is often **no perfectly known** DGP.    
  - Any formula or model we write is an approximation of the **unknowable “truth.”**

---

## Model vs. Reality — The Map Analogy for DGPs

.pull-left[
- **A map ≠ the territory**:  
  - We use maps to navigate, but they are always simplified.  
  - Similarly, a forecast model ≠ reality—it is a *purposeful* simplification.

- **Different maps for different needs**:  
  - A tourist map highlights landmarks, while a transportation map focuses on roads to inform navigation.  
  - Each addresses *specific* questions, just as we build different forecasting models for different objectives.
]

<br>

![](data:image/png;base64,#../../figures/transportation_oxford.png)
]

---

## Why Use DGPs If They Do not Actually Exist?

**(1) Guiding Principle:**    
   - Thinking in terms of a *hypothetical* DGP helps us design or select reasonable model structures.  
   - E.g., we incorporate domain insights: “Does our hotel occupancy data show strong seasonality?”

**(2) Clarifying Assumptions:**    
   - Even if the DGP is not known, stating assumptions (e.g., no trend, constant variance) makes our models testable and improvable.

**(3) Iterative Refinement:**    
   - As new data contradict our assumptions, we adjust our “map” of reality.  
   - In forecasting, we continually update models to capture changing conditions.

---

## Key DGP Takeaways

- **All Models Are Wrong…**  
  - ...but some are *useful* for forecasting, planning, or decision-making.

- **The DGP Is a Useful Fiction**  
  - We talk about it to structure our thinking.  
  - We never truly “see” it; we only see **data**.

- **Practical Implication**  
  - A good model is *close enough* to guide accurate forecasts.  
  - Remain aware of model limitations and be ready to adapt.

---

# "What Can (and Can not) We Forecast?"

---

## Rank these Scenarios in Terms of Forecastability

- **Rank** each scenario (in the next tab) from **easiest** (1) to **hardest** (6) to predict.

- **Submit** your ranking by clicking [here](https://www.menti.com/al4qbc8hg3jnm)

]

- <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#2ecc71;overflow:visible;position:relative;"><path d="M0 112.5V422.3c0 18 10.1 35 27 41.3c87 32.5 174 10.3 261-11.9c79.8-20.3 159.6-40.7 239.3-18.9c23 6.3 48.7-9.5 48.7-33.4V89.7c0-18-10.1-35-27-41.3C462 15.9 375 38.1 288 60.3C208.2 80.6 128.4 100.9 48.7 79.1C25.6 72.8 0 88.6 0 112.5zM288 352c-44.2 0-80-43-80-96s35.8-96 80-96s80 43 80 96s-35.8 96-80 96zM64 352c35.3 0 64 28.7 64 64H64V352zm64-208c0 35.3-28.7 64-64 64V144h64zM512 304v64H448c0-35.3 28.7-64 64-64zM448 96h64v64c-35.3 0-64-28.7-64-64z"/></svg> **Lottery winning numbers for next weekend**

- <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#f1c40f;overflow:visible;position:relative;"><path d="M375.7 19.7c-1.5-8-6.9-14.7-14.4-17.8s-16.1-2.2-22.8 2.4L256 61.1 173.5 4.2c-6.7-4.6-15.3-5.5-22.8-2.4s-12.9 9.8-14.4 17.8l-18.1 98.5L19.7 136.3c-8 1.5-14.7 6.9-17.8 14.4s-2.2 16.1 2.4 22.8L61.1 256 4.2 338.5c-4.6 6.7-5.5 15.3-2.4 22.8s9.8 13 17.8 14.4l98.5 18.1 18.1 98.5c1.5 8 6.9 14.7 14.4 17.8s16.1 2.2 22.8-2.4L256 450.9l82.5 56.9c6.7 4.6 15.3 5.5 22.8 2.4s12.9-9.8 14.4-17.8l18.1-98.5 98.5-18.1c8-1.5 14.7-6.9 17.8-14.4s2.2-16.1-2.4-22.8L450.9 256l56.9-82.5c4.6-6.7 5.5-15.3 2.4-22.8s-9.8-12.9-17.8-14.4l-98.5-18.1L375.7 19.7zM269.6 110l65.6-45.2 14.4 78.3c1.8 9.8 9.5 17.5 19.3 19.3l78.3 14.4L402 242.4c-5.7 8.2-5.7 19 0 27.2l45.2 65.6-78.3 14.4c-9.8 1.8-17.5 9.5-19.3 19.3l-14.4 78.3L269.6 402c-8.2-5.7-19-5.7-27.2 0l-65.6 45.2-14.4-78.3c-1.8-9.8-9.5-17.5-19.3-19.3L64.8 335.2 110 269.6c5.7-8.2 5.7-19 0-27.2L64.8 176.8l78.3-14.4c9.8-1.8 17.5-9.5 19.3-19.3l14.4-78.3L242.4 110c8.2 5.7 19 5.7 27.2 0zM256 368a112 112 0 1 0 0-224 112 112 0 1 0 0 224zM192 256a64 64 0 1 1 128 0 64 64 0 1 1 -128 0z"/></svg> **Sunrise time in Oxford, Ohio on January 1, 2026**

- <svg aria-hidden="true" role="img" viewBox="0 0 320 512" style="height:1em;width:0.62em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#e74c3c;overflow:visible;position:relative;"><path d="M160 64c-26.5 0-48 21.5-48 48V276.5c0 17.3-7.1 31.9-15.3 42.5C86.2 332.6 80 349.5 80 368c0 44.2 35.8 80 80 80s80-35.8 80-80c0-18.5-6.2-35.4-16.7-48.9c-8.2-10.6-15.3-25.2-15.3-42.5V112c0-26.5-21.5-48-48-48zM48 112C48 50.2 98.1 0 160 0s112 50.1 112 112V276.5c0 .1 .1 .3 .2 .6c.2 .6 .8 1.6 1.7 2.8c18.9 24.4 30.1 55 30.1 88.1c0 79.5-64.5 144-144 144S16 447.5 16 368c0-33.2 11.2-63.8 30.1-88.1c.9-1.2 1.5-2.2 1.7-2.8c.1-.3 .2-.5 .2-.6V112zM208 368c0 26.5-21.5 48-48 48s-48-21.5-48-48c0-20.9 13.4-38.7 32-45.3V208c0-8.8 7.2-16 16-16s16 7.2 16 16V322.7c18.6 6.6 32 24.4 32 45.3z"/></svg> **Maximum temperature in Oxford, Ohio tomorrow**

- <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#9b59b6;overflow:visible;position:relative;"><path d="M349.4 44.6c5.9-13.7 1.5-29.7-10.6-38.5s-28.6-8-39.9 1.8l-256 224c-10 8.8-13.6 22.9-8.9 35.3S50.7 288 64 288H175.5L98.6 467.4c-5.9 13.7-1.5 29.7 10.6 38.5s28.6 8 39.9-1.8l256-224c10-8.8 13.6-22.9 8.9-35.3s-16.6-20.7-30-20.7H272.5L349.4 44.6z"/></svg> **Daily electricity demand in 3 days**

]

]

---

## Perfect (or Near-Perfect) Forecasts

- **Examples**  
  1. **Sunset Times**:  
     - Based on precise astronomical calculations.  
     - We can predict sunset to the exact minute, *tomorrow* or even a year from now.  
  2. **Tides**:  
     - Governed by well-modeled gravitational forces of the Moon and Sun.  
     - Highly predictable for centuries into the future.

- **Why So Certain?**  
  - These phenomena follow *deterministic* (or near-deterministic) physical laws.  
  - Little to no stochastic “noise” in the process.

---

## Partially Predictable — Weather & Markets

- *Tomorrow’s Forecast*: Quite accurate (initial conditions + physical models).

- *1 Year Ahead*: Chaos and changing conditions degrade accuracy significantly.  
]

- *Tomorrow’s Close*: Some short-term signals exist, but accuracy is limited (especially if you are attempting to beat the market; accuracy is relatively high if you just want to be in the ball park of the `adjusted close`).

- *1 Year Ahead*: Many unknown macro shocks, making precise forecasts very uncertain.
]

---

## Unpredictable — Lottery Numbers

- **No Predictable Pattern**  
  - Draws are *engineered* to be random.  
  - No matter how much data you collect, you can’t *outpredict* chance.

- **Why “Un-forecastable”?**  
  - The Data-Generating Process (DGP) is effectively *pure noise* by design.  
  - No structural or deterministic component to model.  
]

]

---

## Relating It Back to the DGP

- **Different Types of DGPs**  
  1. **Deterministic (or nearly so)**: Sunset times, tidal schedules.  
  2. **Complex & Partly Stochastic**: Weather, financial markets.  
  3. **Pure Randomness**: Lottery draws.

- **Key Lesson**  
  - *All* these processes have a DGP—some are more “knowable” than others.  
  - *Forecastability* depends on how much of that DGP is deterministic vs. random and how well we can model it.

---

# Key Forecasting Terms

---

## Forecasting

- **Forecasting** is the process of using *historical data* and *patterns* to predict *future* values or events.

- The objective of most **time series analyses** is to provide forecasts of future values of the time series.

---

## Explanatory Forecasting

- In addition to past data, **explanatory forecasting** uses *additional variables* to predict future values of the variable(s) of interest. To make the forecasts, we need to include both historical and future predictions for each of the explanatory variables. For example,   
  - **Forecasting electricity demand** using weather forecasts, time of day, day of week, etc.
  
.pull-left[
![](data:image/png;base64,#../../figures/cell-7-output-1.png)
]

**Image Sources:** Nixtla's demo for forecasting the remaining useful life of an engine using exogenous sensor data. See  [here](https://nixtlaverse.nixtla.io/neuralforecast/docs/getting-started/introduction.html) for more details. 
]

---

## Backtesting

- Backtesting is the practice of **evaluating** a forecasting model by applying it to **historical data** and comparing the predictions with the actual outcomes.   
- A way to see how the model **would have performed** in the past.  
- Backtesting is the time series equivalent of a **train-test split** in ML; **not random though**.

**Image Source:** [Chained Windows](https://github.com/Nixtla/statsforecast/blob/main/nbs/imgs/ChainedWindows.gif) from Nixtla's GitHub Repo for *statsforecast*. 
]

---

## Insample vs. Out-of-Sample Metrics

- **In-Sample Metrics**:  
  - Metrics calculated on the **same data** used to train the model.  
  - Can be misleading, as the model has already seen this data.  
  
- **Out-of-Sample Metrics**:
  - Metrics calculated on **data not seen by the model** during training (i.e., test/holdout/out-of-sample data).  
  - More reliable indicators of how the model will perform on new data.

---

# Recap

---

# Summary of Main Points

By now, you should be able to do the following:

- Describe the role of forecasting in business.

- Describe the key components of a **time-series** (**trend**, **seasonality**, **multiple seasonality**, and **cycles**).

- Explain the concept of data-generating process (DGP)

- Discuss limits of forecasting

- Understand key forecasting terminology

---

# 📝 Review and Clarification 📝

1. **Class Notes**: Take some time to revisit your class notes for key insights and concepts.
2. **Zoom Recording**: The recording of today's class will be made available on Canvas approximately 3-4 hours after the session ends.
3. **Questions**: Please don't hesitate to ask for clarification on any topics discussed in class. It's crucial not to let questions accumulate.

---

# 📖 Recommended Readings 📖

#### 🐍 Python Prep

- [Getting Started with Conda](https://conda.io/projects/conda/en/latest/user-guide/getting-started.html)
- [Data Structures](https://docs.python.org/3/tutorial/datastructures.html)

#### 🤖 LLM: Prep

- [A Very Gentle Introduction to Large Language Models without the Hype](https://mark-riedl.medium.com/a-very-gentle-introduction-to-large-language-models-without-the-hype-5f67941fa59e)

---

# 🎯 Assignment 🎯

- Go over your notes and complete [Assignment 01](https://miamioh.instructure.com/courses/240425/quizzes/741952) on Canvas.